We'll write the equation of the line into the slope intercept form:
y=mx+n, where m is the slope of the line and n is the y intercept.
We need to put the equations in this form to determine their slopes. We'll use the property of slopes of 2 perpendicular lines: the product of the values of the slopes of 2 perpendicular lines is -1.
Let's suppose that the 2 slopes are m1 and m2.
We'll determine m1 from the given equation of the line, that is perpendicular to the one with the unknown equation.
The equation is -x+4y-3=0.
We'll isolate 4y to the left side. For this reason, we'll subtract -x - 3 both sides:
4y = x + 3
We'll divide by 4:
y = x/4 + 3/4
The slope m1 = 1/4.
We also know that the line passes through the point (-2,1), so the equation of a line that passes throuh a given point and it has a known slope is:
We'll remove the brackets and we'll move all terms to one side:
y - 1 + 4x + 8 = 0
We'll combine like terms and we'll get the equation of the requested line: y + 4x + 7 = 0